Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Degeneracy in NLP and the development of results motivated by its presence

We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. Ideal nondegeneracy at a local minimizer is taken to mean satisfaction of second order sufficient conditions, linear independence and strict complimentary slackness. Following a brief exploration of the relationship of these conditions with the classical definition of nondegeneracy in linear programming, we recall a number of optimality and regularity conditions used to attempt to resolve degeneracy and survey results of Fiacco, McCormick, Robinson, Kojima, Gauvin and Janin, Shapiro, Kyparisis and Liu. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.Research supported by National Science Foundation Grant ECS 90-00560 and Grant N00014-89-J-1537 Office of Naval Research     

The effect of UV light on the thermooxidative stability of linear low density polyethylene films crosslinked by ionizing radiation

The effect of ultraviolet (UV) light on the thermooxidative stability of Linear Low Density Polyethylene(LLDPE) films was studied. LLDPE was stabilized with phenolic type antioxidant known as Irganox 1010, hindered amine light stabilizer known as Chimmasorb 944 and phenolic type gamma stabilizer. The influence of these additives on the thermooxidative stability of gamma and UV irradiated LLDPE were investigated by isothermal Differential Scanning Calorimeter (DSC). The oxidation induction time (OIT) experiments indicate that antirad free LLDPE films which contains antioxidant and UV stabilizer are more sensitive to gamma and UV radiation. On the other hand, films which contain antirad and irradiated to different doses of γ-radiation demonstrated improved thermooxidative stability.     

线性时滞系统实用稳定性的一个简明判据

利用比较的方法，获得了线性时滞系统实用稳定性的一个简单判定定理．     

分子筛笼内金属羰基簇合物的热稳定性研究

本实验采用戊马比妥钠诱发豚鼠和家兔急性心力衰竭模型，观察了舒心丸的治疗作用。结果表明，舒心丸ｉｖ能明显升高心衰豚鼠的心脏收缩幅度和心衰家兔的Ｂｐ，ＬＶＰ，ＬＶ±ｄｐ／ｄｔ和ＣＯ。其作用与哇巴因相似。     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

Chiral recognition in the resolution of enantiomers by GLC

Summary Chiral recognition of many enantiomeric solutes by a chiral amide stationary phase is based mainly on hydrogen bonding. A chiral-recognition-factor CHI is proposed, given by the difference of the enthalpy change in the enantiomer discrimination, standardized with respect to the specific interaction of the solutes with the diamide core of the stationary phase. The r?le of the entropy part is also discussed. By extrapolation of the retention behaviour to elevated temperature, peak inversion of enantiomers is predicted. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

TCDD的密度泛函理论研究

用B3LYP/6-311G~(**)方法全优经计算22个四氯二苯并对二（左口右恶）英（ 简称TCDD）分子，得到几何构型、总能量、标准熵、标准焓和标准自由能。将2， 3，7，8－TCDD的计算构型与X射线衍射实验测定值进行了比较。计算结果表明，总 能量、标准焓和标准自由能与氯原子量换位置的相关性很高（r > 0.997）.1,3,6, 8-TCDD的总能量处自由能最低，即最稳定，以此参照，得到异构体的总能量的相对 稳定性顺序和自由能的相对稳定性顺序。1,3,7,9－TCDD的稳定性次之，1,3,7,8- TCDD居第三，将这二个顺序与焚烧炉产生的TCDD异构体和合成的异构体对的生成面 分比进行了比较，说明焚烧炉中产生的TCDD和合成的TCDD对的分布主要受热力学控 制。     

Structure,Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, I _h , D _2h , T). Our results demonstrate that it is possible to create two new families of nested chiral icosahedral (I) fullerenes namely C₂₆₀@C₅₆₀@C₉₈₀@C₁₅₂₀@, ...,and C₁₄₀@C₃₈₀@C₇₄₀@C₁₂₂₀@ ..., which exhibit interlayer separations of ca. 3.4 Å. These chiral fullerenes are thought to possess metalliclike conduction properties. We discuss in detail the transformation of polyhedral graphitic particles into quasispherical nested giant fullerenes by reorganization of carbon atoms, which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed under extreme conditions, such as those produced by high-energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.